1. ## Find the Limit

Hey all, sorry for bugging you again but I have another question...

I've been doing them right so far, so I'm confused as to why this one's supposedly wrong.

The question is: Evaluate the limit for:

lim x-->3 squareroot(x+1)-2 / x-3

So, I multipled the top and bottom by the conjugate of the numerator and got

lim x-->3 (squareroot(x+1)-2)(squareroot(x+1)+2) / (x-3)(squareroot(x+1)+2)
lim x-->3 (x+1)-4 / (x-3)(squareroot(x+1)+2)
lim x-->3 (x-3) / (x-3)(squareroot(x+1)+2) and I cancelled the (x-3) from top and bottom

I then plugged 3 into (squareroot(x+1)+2) to get (squareroot(4)+2) which is 2+2 = 4

However, it says the answer is wrong. I'm really not sure why.

Help is appreciated! Thanks.

2. Originally Posted by dark-ryder341
Hey all, sorry for bugging you again but I have another question...

I've been doing them right so far, so I'm confused as to why this one's supposedly wrong.

The question is: Evaluate the limit for:

lim x-->3 squareroot(x+1)-2 / x-3

So, I multipled the top and bottom by the conjugate of the numerator and got

lim x-->3 (squareroot(x+1)-2)(squareroot(x+1)+2) / (x-3)(squareroot(x+1)+2)
lim x-->3 (x+1)-4 / (x-3)(squareroot(x+1)+2)
lim x-->3 (x-3) / (x-3)(squareroot(x+1)+2) and I cancelled the (x-3) from top and bottom

I then plugged 3 into (squareroot(x+1)+2) to get (squareroot(4)+2) which is 2+2 = 4

However, it says the answer is wrong. I'm really not sure why.

Help is appreciated! Thanks.
$\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 1} - 2}}
{{x - 3}} = \mathop {\lim }\limits_{x \to 3} \frac{{\left( {\sqrt {x + 1} - 2} \right)\left( {\sqrt {x + 1} + 2} \right)}}
{{\left( {x - 3} \right)\left( {\sqrt {x + 1} + 2} \right)}} =$

$= \mathop {\lim }\limits_{x \to 3} \frac{{x + 1 - 4}}
{{\left( {x - 3} \right)\left( {\sqrt {x + 1} + 2} \right)}} = \mathop {\lim }\limits_{x \to 3} \frac{{x - 3}}
{{\left( {x - 3} \right)\left( {\sqrt {x + 1} + 2} \right)}} =$

$= \mathop {\lim }\limits_{x \to 3} \frac{1}{{\sqrt {x + 1} + 2}} = \frac{1}{{\sqrt {3 + 1} + 2}} = \frac{1}{4}.$

3. Oh wow, I feel silly! Thanks for showing me.